The former first lady also talked about the importance of the Duchess choosing something she felt passionate about.
Sandberg famously advocated for women to take charge in the workplace in her 2013 book "Lean In".
"Like me, Meghan probably never dreamt that she'd have a life like this, and the pressure you feel-from yourself and from others-can sometimes feel like a lot", the Becoming author says in Good Housekeeping's January issue.
Earlier in the day she encouraged some London schoolgirls to ensure they played a role in tackling the "the bitterness, the nastiness that we see in politics" by never wasting their vote.
Ms Obama apologised to the crowd for swearing, telling the audience she'd forgotten where she was at that moment. The impressive list of moderators includes Oprah, Tracee Ellis Ross, Chimamanda Ngozi Adichie, former senior adviser to President Obama Valerie Jarrett, and more.
Obama's comments are not the first criticism of Sandberg's approach, which is accused of suggesting that individual women have to be the solution to workplace inequality rather than widespread policy changes.
Speaking after the event, Winnie, who had been on stage interviewing Mrs Obama, told the Gazette: "I was so nervous beforehand but speaking to her just made us feel so comfortable".
Michelle Obama has said the Queen branded royal protocol "rubbish" during a visit to Windsor Castle.
"We are by no means suggesting Sandberg intended to blame women for inequality", researchers wrote. The circles have been touted as "one of the few places in the world where women can be overtly, unapologetically ambitious", according to the New York Times.
More recently, "leaning in" and Sandberg's leadership were placed under additional scrutiny after controversy erupted around Facebook and Russian interference in the 2016 election.
On social media, Obama's words were met with widespread approval.
It was not just children but "teachers who underestimated me every step of the way".
Michelle Obama this afternoon told Elizabeth Garrett Anderson students that her decade-long relationship with the Barnsbury school was one of her proudest achievements.
"Imagine being your age and have your father criticised in public, having everything you say and post analysed, your first boyfriend plastered all over the tabloids or going to prom with men with guns, going to soccer practice and people taking pictures of you because of who you are".